[Lemma 6.1 of [1]}]
Let \(\lbrace _m\rbrace \)  and \(\lbrace _m\rbrace \)  be sequences of random vectors. If \(\Vert _m\Vert  = _{}(A_m)\)  conditional on \(\lbrace _m\rbrace \)  for a sequence of positive constants \(\lbrace A_m\rbrace \) , then \(\Vert _m\Vert  = _{}(A_m)\)  unconditionally.
